Spatial rainbows and catastrophes in transmission of protons through electrostatic octopole lens

Abstract

This paper considers transmission of initial parallel proton beam with kinetic energy of 10 k?V through electrostatic octopole lens. The spatial rainbows and corresponding proton distributions are calculated by using infinite length approximation potential. Positive potentials of the lens electrodes are set to be 0.35 kV and 9 kV. It has been shown that by application of catastrophe theory, generating function for mapping proton positions between entrance and exit transverse plains can be determined, giving accurate rainbow patterns for biasing potentials of 0,35 kV.